f(x) = 3/8x + 7. Find f^-1(f(6))?

Answer 1

The above contributor is completely incorrect.

"Helmut: f^-1(x) = 8(x - 7)/3
f^-1(x) = 8(6 - 7)/3 = -8/3
55 minutes ago - Report Abuse "

Terrible. Not only did Helmut incorrectly take the inverse, but he didn't even plug in the proper number into the [incorrect] inverse equation. In the problem, I assumed the first term in f(x) was "three-eighths x" because it worked out much neater that "three over eight x", but nevertheless, you DO NOT, I repeat DO NOT find the inverse by simply inverting the fraction.

Helmut's second mistake was trying to find f^-1(6) instead of f^-1(f(6)). You need to plug 6 into the f(x) equation, and then plug in that answer into the inverse equation.

Please disregard the above incorrect answer, and without further ado, here is how you do the problem:





f(x) = 3/8x + 7

To find the inverse:

y = 3/8x + 7 (switch variables and solve for y to find equation of the the inverse)
x = 3/8y + 7
x - 7 = 3/8y
8/3(x - 7) = y
y = 8/3x - 56/3

Therefore,
f^-1(x) = 8/3x - 56/3

Now, f^-1(f(6)) is a composite function. First, we need to find f(6).

f(x) = 3/8x + 7
f(6) = 3/8(6) + 7
f(6) = 18/8 + 7
f(6) = 9/4 + 28/4
f(6) = 37/4

And to find f^-1(f(6)),

f^-1(f(6)) = f^-1(37/4)

f^-1(x) = 8/3x - 56/3
f^-1(37/4) = 8/3(37/4) - 56/3
f^-1(37/4) = 8/3(37/4) - 56/3
f^-1(37/4) = 74/3 - 56/3
f^-1(37/4) = 18/3
f^-1(37/4) = 6


Therefore, f^-1(f(6)) = 6.

Answer 2

math_kp
Member since: July 11, 2006
Total points: 10,638 (Level 6)
Points earned this week: 171
32%Best answer
1799 answers
math_kp
0



we have f(x) = 3/8 x + 7

this function being linear is reversible)

( if y = 3/8 x + 7 then 3/8 x = y-7 or x = 3/8(y-7) of f^-(x) = 3/8(x-7))

so f^-1f(x) = x or putting x = 6 we get

f^-1 f(6) = 6
---------- ----------------- --------- -----------


mathkp, that doesnt make any sense. when u found the inverse, u went from f^-(x) = 3/8(x-7)) to f^-1f(x) = x , which doesnt make any sense. it was wrong anyway, but this was icing on the cake.

u made up a fake equation so u could copy someone elses answer. thats sad.

Answer 3

f^-1(x) = 8(x - 7)/3
f^-1(x) = 8(6 - 7)/3 = -8/3

Answer 4

i don't know wat Chris found wrong w/ Hemlut's inverse.
only the value of x substituted was wrong.
y= 3/8x+7
y-7=3x/8
x=8(y-7)/3
f^-1(x)=8(x-7)/3

f(6)= 3*6/8 +7
=37/4
f^-1(37/4)= 8(37/4 -7)/3
=8(9/4)/3
=6
math_kp is absolutely correct:
f^-1(f(x))=x
just like
sin^-1(sinx)=x